# Least Common Multiple

- - Pre-Algebra

The least common multiple (LCM) of two or more numbers is the smallest or least number that is divisible by all the given numbers. Hence, for counting numbers p and q, $p\times q=GCF\left (p,q\right )\times LCM\left (p,q\right ).$

Examples:

1. Find the LCM of 6 and 20.

SOLUTION:

Our LCM is the product of all the quotients and divisors, that is,

2. Find the LCM of 8, 24 and 36.

SOLUTION:

Hence, the least common multiple of 8, 24 and 36 is

3. Find the LCM of 2, 5 and 7.

SOLUTION:

The numbers are relatively prime. Their LCM is just their product; that is,